In this case, considering only the CMB data, a spatially flat background geometry is disfavored at slightly more than 95% CL with the constraint on the curvature parameter reading \(\Omega _{K0}=-0.073^{+0.070}_{-0.086}\)  at 95% CL. Interestingly, a strong preference for a curved spacetime is found combining CMB and Pantheon (from which we get \(\Omega _{K0}=-0.030^{+0.020}_{-0.022}\)  at 95% CL).
Conversely, including the BAO measurements, flatness becomes always consistent within one standard deviation for all the other different data combinations, but these results should be taken with caution because of the data inconsistency in a curved universe. As concerns the dark energy equation of state, using only the CMB data we find that both phantom (\(w<-1\) ) and quintessential behaviors (\(w>-1\) ) are allowed within the 68% CL results. Combining CMB with BAO (+Pantheon) no significant differences are observed, as well. Conversely, it should be noted that the results for CMB+Pantheon (\(w=-1.28^{+0.25}_{-0.28}\)  at 95% CL) suggest a preference for a phantom dark energy at the level of more than 95% CL. As for the baseline \(w\rm {CDM} + \Omega _K\)  model, also in this extended parameter space, allowing phantom models of dark energy does not alleviate the tensions, and from CMB+Pantheon thre is indication for a phantom closed universe, as in [1]}. Indeed the value of the Hubble parameter inferred by the CMB data, \(H_0=52^{+6}_{-16}\)  km/s/Mpc at 68% CL, and the independent measurement provided by the SH0ES collaboration are in tension at the level of \(3.4\sigma \) . This preference for lower values of \(H_0\)  is mostly driven by the degeneracy with the spatial curvature. Indeed, when the BAO data are combined with the CMB, no evidence is found for curvature and the constraints on \(H_0\)  look very different and become similar to the usual results obtained within the flat \(\Lambda \) CDM model. Conversely, for CMB+Pantheon, due to the preference for a curved spacetime of this dataset, we still obtain a lower value \(H_0=60.2\pm 2.6\)  km/s/Mpc at 68% CL, in strong tension with local measurements at about \(4.6 \sigma \) . Finally, it is worth pointing out that in this model the bounds on the total neutrino mass obtained using the Planck measurements (\(M_{\nu }<0.83\)  eV at 95% CL) remain almost unchanged with respected to the previous scenarios, while the bounds for CMB+Pantheon are significantly relaxed to \(M_{\nu }<0.46\)  eV at 95% CL. Anyway, the most significant impact on the bounds on relic neutrinos is obtained by combining CMB and BAO from which we obtain \(M_{\nu }<0.19\)  eV at 95% CL. Considering CMB+BAO+Pantheon all together this bound is robust and almost unchanged.
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